What benefits would i gain from a salt chlorine system and how much does that cost to install?
Primarily, you won't have to add chlorine to your pool during swimming season. Users also notice they're able to maintain algae free pools at slightly lower FC levels than a manually dosed pool. In winter when / if your pool gets colder than 60 degrees, you'll still need to manually dose the pool because the cell will not function in cold water. You'll save time, gas, and money not hauling jugs of bleach from the store, plus no more need to measure and dose the pool. I've had mine running for a few weeks now and notice much what others here on the site mention: now that I've got the settings dialed in, I never worry about missing a day and FC levels falling too low. I even left town from Weds last week til Sunday and FC was up 1.5ppm from when I left. The only thing I really need to monitor anymore is pH because I've dropped my TA numbers as low as it seems they'll go and my pH still rises due to high TA fill water and a pesky air leak somewhere.
Also, most owners notice a silkier, less harsh water feel by adding the 3000-4000 (per manufacturer's spec) PPM of salt to their pool. This is not a high enough concentration to damage any of your equipment or harm swimmers.
Depending on the size of your pool, you'll be looking at $1500-2k for the equipment, and many users here do their own installation. It's pretty easy. There are considerations if your pool is still under warranty, or if there's need for you to pull a permit with your local building authority. You'll pay more if you need someone to do the install. With a pool as large as yours, I'm sure before long you'll understand how much chlorine needs added daily to keep up with the 2-3ppm lost to sunlight. There are a few threads on this site where folks have talked through the "break even" analysis on chemicals cost alone, plus the added time and energy freed up that was being used for testing and dosing with chemical. When you start looking at units, make sure to look for salt cells with a 60,000 gallon capacity. Your pool is very large, and the recommendation here is to buy a salt cell with at least twice the capacity of your pool to reduce wear on the unit itself. You're right at that threshold, so your unit might need to run slightly more than my 60K salt cell, because my pool is 10k gallons less than yours.